Help understanding a change in limits of integration:
Original limits are from sqrt2 to 2. If u=sec(theta), then the new limits become pi/4 to pi/3, respectively. How did these numbers come about?

Question

Help understanding a change in limits of integration:
Original limits are from sqrt2 to 2.  If u=sec(theta), then the new limits become pi/4 to pi/3, respectively.  How did these numbers come about?

anonymous · Answer

I actually see where the pi/3 came from.  Still having trouble seeing where pi/4 came from though...

asnaseer · Answer

$$u=\sec(\theta)=\frac{1}{\cos(\theta)}$$$$\therefore \theta=\cos^{-1}(\frac{1}{u})$$Now put in $u=\sqrt{2}$ and $u=2$ to get the new limits

anonymous · Answer

I was forgetting to rationalize the denominator during u=sqrt2   :3  
Thanks for your help!

asnaseer · Answer

yw :)